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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Continuous Theta Burst Stimulation (cTBS)

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Dr. Rishabh Pathak

Continuous Theta Burst Stimulation (cTBS) is a specific protocol of repetitive transcranial magnetic stimulation (rTMS) that is used to modulate cortical excitability and induce neuroplastic changes in the brain. Here is a detailed explanation of Continuous Theta Burst Stimulation:


1.      Definition:

o   cTBS: Continuous Theta Burst Stimulation is a patterned form of rTMS that involves delivering bursts of magnetic pulses at a specific frequency and intensity over a continuous period of time to a targeted area of the brain. It is characterized by the application of theta-burst patterns of stimulation.

2.     Stimulation Parameters:

o   Theta Burst Pattern: The theta burst pattern consists of bursts of three pulses at 50 Hz repeated at a theta frequency (5 Hz). This pattern is delivered continuously over a specified duration, typically ranging from several seconds to minutes, depending on the research or clinical protocol.

o   Intensity and Duration: The intensity of cTBS is usually set as a percentage of the individual's resting motor threshold, ensuring that the stimulation is tailored to the specific cortical excitability of the target area. The duration of cTBS can vary based on the desired effects and experimental design.

3.     Mechanism of Action:

o   Inhibitory Effect: cTBS is primarily known for its inhibitory effects on cortical excitability. By delivering continuous theta burst patterns, the stimulation leads to a reduction in neuronal firing rates and synaptic transmission in the targeted brain region.

o   Long-Lasting Effects: cTBS has been shown to induce long-lasting changes in cortical excitability, with inhibitory effects persisting beyond the stimulation period. This ability to modulate neural activity and induce plastic changes makes cTBS a valuable tool for studying brain function and potential therapeutic applications.

4.    Applications:

o   Research: cTBS is widely used in research settings to investigate the role of inhibitory mechanisms in cortical function, neural plasticity, and motor learning. Researchers utilize cTBS to study the effects of cortical inhibition on cognitive processes, motor control, and sensory functions.

o Therapeutic Potential: In clinical applications, cTBS is being explored as a potential treatment strategy for neurological and psychiatric disorders. By modulating cortical excitability and neural networks, cTBS may offer therapeutic benefits for conditions such as depression, chronic pain, stroke recovery, and movement disorders.

5.     Clinical Studies:

o  Depression: cTBS has shown promise as a non-invasive treatment for depression, particularly in individuals who are resistant to traditional therapies. By targeting specific brain regions implicated in mood regulation, cTBS may help alleviate depressive symptoms and improve overall well-being.

o  Neurorehabilitation: In the field of neurorehabilitation, cTBS is being investigated as a potential adjunct therapy to enhance motor recovery following stroke, traumatic brain injury, or other neurological conditions. By modulating cortical plasticity, cTBS may facilitate motor relearning and functional recovery.

In summary, Continuous Theta Burst Stimulation is a specialized form of rTMS that exerts inhibitory effects on cortical excitability and induces long-lasting changes in neural activity. With applications in research and clinical settings, cTBS offers insights into brain function, neuroplasticity, and potential therapeutic interventions for a range of neurological and psychiatric disorders.

 

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